{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Plotting the Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "sns.set(context=\"notebook\", style=\"whitegrid\", palette=\"dark\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>population</th>\n",
       "      <th>profit</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>6.1101</td>\n",
       "      <td>17.5920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.5277</td>\n",
       "      <td>9.1302</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>8.5186</td>\n",
       "      <td>13.6620</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>7.0032</td>\n",
       "      <td>11.8540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.8598</td>\n",
       "      <td>6.8233</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   population   profit\n",
       "0      6.1101  17.5920\n",
       "1      5.5277   9.1302\n",
       "2      8.5186  13.6620\n",
       "3      7.0032  11.8540\n",
       "4      5.8598   6.8233"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv('ex1data1.txt', names=['population', 'profit'])\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.FacetGrid at 0x7f33a5d4b650>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ShQFlZpWeLwUAQE1UPM08Tij4CQCNR0AVoOAn6oUvQkB5DN0VoOAn6iH7Rah/z4DGxtK5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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f33d1b80c10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 输出样本文件分布图\n",
    "%matplotlib inline\n",
    "sns.lmplot('population', 'profit', data, size=6, fit_reg=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Gradient Descent"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![avatar](img/1.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 代价函数\n",
    "def cost(theta, X, Y):\n",
    "    \"\"\"\n",
    "    @param X: 样本集; m*n的矩阵，m为样本个数，n为样本特征个数，其中x0 = 1\n",
    "    @param Y: 样本结果;m*1的矩阵，\n",
    "    @param theta: 带求解的最佳θ; 1*n的矩阵\n",
    "    \"\"\"\n",
    "    m, n = np.shape(X)\n",
    "    # h(x^i) - y^i\n",
    "    inner = np.dot(X, theta.T) - Y\n",
    "    squareSum = np.dot(inner.T, inner)\n",
    "    return squareSum / (2 * m)\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![avatar](img/2.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 梯度函数\n",
    "def gradient(theta, X, Y):\n",
    "    m, n = np.shape(X)\n",
    "    inner = np.dot(X, theta.T) - Y\n",
    "    # xj^1 * inner^1 + xj^2 * inner^2 + ... + xj^m * inner^m\n",
    "    val = np.dot(X.T, inner)  # val为n*1的矩阵\n",
    "    return val.T / m\n",
    "\n",
    "\n",
    "# 梯度下降\n",
    "def gradientDecent(theta, X, Y, alpha, times):\n",
    "    \"\"\"\n",
    "    @param alpha: 学习率\n",
    "    @param times: 重复次数\n",
    "    \"\"\"\n",
    "    for i in range(times):\n",
    "        theta = theta - alpha * gradient(theta, X, Y)\n",
    "        c = cost(theta, X, Y)\n",
    "        print \"%d: theta=%s, cost=%f\" %(i, theta, c.item())\n",
    "    return theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0: theta=[[ 0.05839135  0.6532885 ]], cost=6.737190\n",
      "1: theta=[[ 0.06289175  0.77000978]], cost=5.931594\n",
      "2: theta=[[ 0.05782293  0.79134812]], cost=5.901155\n",
      "3: theta=[[ 0.05106363  0.79572981]], cost=5.895229\n",
      "4: theta=[[ 0.04401438  0.79709618]], cost=5.890095\n",
      "5: theta=[[ 0.03692413  0.79792547]], cost=5.885004\n",
      "6: theta=[[ 0.02983712  0.79865824]], cost=5.879932\n",
      "7: theta=[[ 0.02276118  0.79937279]], cost=5.874879\n",
      "8: theta=[[ 0.0156977   0.80008305]], cost=5.869844\n",
      "9: theta=[[ 0.0086469  0.8007915]], cost=5.864827\n",
      "10: theta=[[ 0.00160879  0.80149857]], cost=5.859828\n",
      "11: theta=[[-0.00541662  0.80220436]], cost=5.854847\n",
      "12: theta=[[-0.01242938  0.80290886]], cost=5.849884\n",
      "13: theta=[[-0.01942949  0.8036121 ]], cost=5.844939\n",
      "14: theta=[[-0.02641699  0.80431407]], cost=5.840011\n",
      "15: theta=[[-0.03339189  0.80501478]], cost=5.835102\n",
      "16: theta=[[-0.04035421  0.80571422]], cost=5.830210\n",
      "17: theta=[[-0.04730399  0.8064124 ]], cost=5.825336\n",
      "18: theta=[[-0.05424124  0.80710932]], cost=5.820479\n",
      "19: theta=[[-0.06116598  0.80780498]], cost=5.815640\n",
      "20: theta=[[-0.06807824  0.8084994 ]], cost=5.810818\n",
      "21: theta=[[-0.07497804  0.80919256]], cost=5.806013\n",
      "22: theta=[[-0.08186541  0.80988447]], cost=5.801226\n",
      "23: theta=[[-0.08874035  0.81057513]], cost=5.796456\n",
      "24: theta=[[-0.09560291  0.81126455]], cost=5.791704\n",
      "25: theta=[[-0.10245309  0.81195272]], cost=5.786968\n",
      "26: theta=[[-0.10929093  0.81263966]], cost=5.782250\n",
      "27: theta=[[-0.11611644  0.81332535]], cost=5.777548\n",
      "28: theta=[[-0.12292965  0.81400981]], cost=5.772863\n",
      "29: theta=[[-0.12973057  0.81469304]], cost=5.768196\n",
      "30: theta=[[-0.13651924  0.81537504]], cost=5.763545\n",
      "31: theta=[[-0.14329567  0.8160558 ]], cost=5.758911\n",
      "32: theta=[[-0.15005988  0.81673534]], cost=5.754293\n",
      "33: theta=[[-0.15681191  0.81741365]], cost=5.749692\n",
      "34: theta=[[-0.16355176  0.81809075]], cost=5.745108\n",
      "35: theta=[[-0.17027946  0.81876662]], cost=5.740540\n",
      "36: theta=[[-0.17699503  0.81944127]], cost=5.735989\n",
      "37: theta=[[-0.1836985  0.8201147]], cost=5.731454\n",
      "38: theta=[[-0.19038988  0.82078693]], cost=5.726935\n",
      "39: theta=[[-0.1970692   0.82145794]], cost=5.722433\n",
      "40: theta=[[-0.20373649  0.82212774]], cost=5.717947\n",
      "41: theta=[[-0.21039175  0.82279633]], cost=5.713477\n",
      "42: theta=[[-0.21703502  0.82346372]], cost=5.709023\n",
      "43: theta=[[-0.22366631  0.8241299 ]], cost=5.704586\n",
      "44: theta=[[-0.23028565  0.82479489]], cost=5.700164\n",
      "45: theta=[[-0.23689305  0.82545867]], cost=5.695758\n",
      "46: theta=[[-0.24348855  0.82612126]], cost=5.691368\n",
      "47: theta=[[-0.25007216  0.82678266]], cost=5.686994\n",
      "48: theta=[[-0.2566439   0.82744286]], cost=5.682635\n",
      "49: theta=[[-0.26320379  0.82810187]], cost=5.678293\n",
      "50: theta=[[-0.26975186  0.8287597 ]], cost=5.673965\n",
      "51: theta=[[-0.27628812  0.82941634]], cost=5.669654\n",
      "52: theta=[[-0.2828126   0.83007179]], cost=5.665358\n",
      "53: theta=[[-0.28932533  0.83072607]], cost=5.661078\n",
      "54: theta=[[-0.29582631  0.83137916]], cost=5.656812\n",
      "55: theta=[[-0.30231557  0.83203108]], cost=5.652563\n",
      "56: theta=[[-0.30879314  0.83268182]], cost=5.648328\n",
      "57: theta=[[-0.31525902  0.83333139]], cost=5.644109\n",
      "58: theta=[[-0.32171326  0.83397978]], cost=5.639905\n",
      "59: theta=[[-0.32815586  0.83462701]], cost=5.635716\n"
     ]
    },
    {
     "data": {
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XMGXiEGw2m98EDvX7GwNpvZp9AjCzxyeEVTSoOkUptU8p9b1SapNSKrARK0FI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\nuAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f33a5c0a490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def main1():\n",
    "    # 获取X，并设置x0=1\n",
    "    ones = pd.DataFrame({'ones': np.ones(len(data))})\n",
    "    X = pd.concat([ones, data], axis=1).iloc[:, :-1].as_matrix()\n",
    "    # 获取Y\n",
    "    Y = data.iloc[:, -1:].as_matrix()\n",
    "    # 初始化theta\n",
    "    theta = np.zeros((1, X.shape[1]))\n",
    "    # 初始化alpha\n",
    "    alpha = 0.01\n",
    "    final_theta = gradientDecent(theta, X, Y, alpha, 60)[0]\n",
    "    \n",
    "    plt.scatter(data.population, data.profit, label=\"Training data\")\n",
    "    plt.plot(data.population, data.population*final_theta[1] + final_theta[0], label=\"Prediction\")\n",
    "    plt.legend(loc=2)\n",
    "\n",
    "    \n",
    "    \n",
    "main1()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Linear regression with multiple variables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![avatar](img/3.png)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>square</th>\n",
       "      <th>bedrooms</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2104</td>\n",
       "      <td>3</td>\n",
       "      <td>399900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1600</td>\n",
       "      <td>3</td>\n",
       "      <td>329900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2400</td>\n",
       "      <td>3</td>\n",
       "      <td>369000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1416</td>\n",
       "      <td>2</td>\n",
       "      <td>232000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3000</td>\n",
       "      <td>4</td>\n",
       "      <td>539900</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   square  bedrooms   price\n",
       "0    2104         3  399900\n",
       "1    1600         3  329900\n",
       "2    2400         3  369000\n",
       "3    1416         2  232000\n",
       "4    3000         4  539900"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv('ex1data2.txt', names=['square', 'bedrooms', 'price'])\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>square</th>\n",
       "      <th>bedrooms</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.130010</td>\n",
       "      <td>-0.223675</td>\n",
       "      <td>0.475747</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.504190</td>\n",
       "      <td>-0.223675</td>\n",
       "      <td>-0.084074</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.502476</td>\n",
       "      <td>-0.223675</td>\n",
       "      <td>0.228626</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.735723</td>\n",
       "      <td>-1.537767</td>\n",
       "      <td>-0.867025</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.257476</td>\n",
       "      <td>1.090417</td>\n",
       "      <td>1.595389</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     square  bedrooms     price\n",
       "0  0.130010 -0.223675  0.475747\n",
       "1 -0.504190 -0.223675 -0.084074\n",
       "2  0.502476 -0.223675  0.228626\n",
       "3 -0.735723 -1.537767 -0.867025\n",
       "4  1.257476  1.090417  1.595389"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 使用方法二进行特征归一\n",
    "def normalizeFeatures(data):\n",
    "    return data.apply(lambda column: (column - column.mean()) / column.std())\n",
    "\n",
    "\n",
    "data = normalizeFeatures(data)\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0: theta=[[ -8.74005360e-19   8.36796367e-03   4.32851306e-03]], cost=0.480549\n",
      "1: theta=[[ -1.77163249e-18   1.66303056e-02   8.56880107e-03]], cost=0.471986\n",
      "2: theta=[[ -2.69288138e-18   2.47885430e-02   1.27223064e-02]], cost=0.463665\n",
      "3: theta=[[ -3.59050851e-18   3.28441704e-02   1.67904489e-02]], cost=0.455578\n",
      "4: theta=[[ -4.39364857e-18   4.07986599e-02   2.07746264e-02]], cost=0.447719\n",
      "5: theta=[[ -5.19678863e-18   4.86534616e-02   2.46762151e-02]], cost=0.440082\n",
      "6: theta=[[ -5.97630692e-18   5.64100037e-02   2.84965695e-02]], cost=0.432659\n",
      "7: theta=[[ -6.87393405e-18   6.40696932e-02   3.22370232e-02]], cost=0.425444\n",
      "8: theta=[[ -7.91329177e-18   7.16339158e-02   3.58988891e-02]], cost=0.418431\n",
      "9: theta=[[ -8.78729713e-18   7.91040367e-02   3.94834595e-02]], cost=0.411614\n",
      "10: theta=[[ -9.75578956e-18   8.64814003e-02   4.29920067e-02]], cost=0.404987\n",
      "11: theta=[[ -1.06770384e-17   9.37673313e-02   4.64257830e-02]], cost=0.398545\n",
      "12: theta=[[ -1.15038003e-17   1.00963134e-01   4.97860214e-02]], cost=0.392282\n",
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     ]
    }
   ],
   "source": [
    "def main2():\n",
    "    # 获取X, 设置x0 = 1\n",
    "    ones = pd.DataFrame({'ones': np.ones(len(data))})\n",
    "    X = pd.concat([ones, data], axis=1).iloc[:, :-1].as_matrix()\n",
    "    # 获取Y\n",
    "    Y = data.iloc[:, -1:].as_matrix()\n",
    "    # 初始化theta\n",
    "    theta = np.zeros((1, X.shape[1]))\n",
    "    # 初始化alpha\n",
    "    alpha = 0.01\n",
    "    final_theta = gradientDecent(theta, X, Y, alpha, 500)[0]\n",
    "    return final_theta\n",
    "    \n",
    "final_theta = main2()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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MJpHJZDAyMoK9e/du6wdqFieiM7vEVBRFRKNR5PN58DyPcDhs65fMDTAMU9X5w1y1l8/n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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f33a4054e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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MMrfuPMBisfBvfuOT/OxPPZd9nLYtoJfwGR3xPfXUU9y/f9/Q18jlwAtfMaPq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JJWeZtJhygF6WhHa2srVqt1x/zOd1EauxVfjUIQhBXjFIVP0Xq9vqyFo9Re10aFM4IgEAgE8Hg8\nuayyB6EaWk28InX9EK/jRk0Pthq1YDdWjTDfaDTK/Pw8Op0Oh8NR8WsvDvDXYnxQKexWfHnYrfh2\nGmQyWa6SE2NC0ul0jgiDwWCuvSglwmKDyVJbJhHScQAxIaCcRUi0T5PJZHR0dOSEOjsdUvFKT0/P\niocAhUKBwWDItQYLW6Rerzcn/Ci8htsp7qkVu7FilXWhn+vS0lJZYb5SRWW1qrxajw/axeawS3w7\nCEqlErPZnIsHEoUGIhm6XC4SiUReVVhK7KJQKDAajTkBQKFwRlyEROGMRqPJ+Ws+KCGqkC9eWU8c\nTamFXDooLmYXlvP7qDSkdmOdnZ01Wa1II69EFO4X+ny+vNxCuVxOMBjMZTVWWlEpVseCIDA4OLhj\nfXF3sTp2W50PGDKZDNFoNEeG0Wh0wy050b3G7/cTCoWQyWRFfTRrsb23FrbKeUW8htI2qSAIFd/r\nEiEIQm4u9EGxGxM/02JVLf6eCp17NnMNpe37pqYmmpubd9x1+9znPsf58+fx+/00NjbyK7/yK3zy\nk5/c7tPaTuyqOh9WbMaHNB6P43K5EAQhlwpR6KNZLeFMNSG2a7fLeUUaRFu417UZY3NRXfsg2Y3B\nfbGRVqvFbrejVCrzrqH450bDfMX4oHQ6TVdX1wMzsrKLXeLbhQRr+ZCmUin+7M/+jJ6eHp588knM\nZvOqhtrS1lQx4Uylo3I2ilp1XilnPnO17D3p+7Lb7TtSXVsM0vflcDhyLeViKDQ3l/ppFpKh9NoE\ng0HcbjdWq7WiStdd1AR2iW8XqyOVShEKhXj++ef52te+xujoKD/3cz9HU1PTunxIYaWPZi1EDe00\n55XC+Uxp9p60vSfu5el0ulw19CAgFosxPz+PRqPB4XBs6H2VCvP98z//c7RaLb29vXR1dXHq1KlV\nSXUXOxa7xLeLtfGtb32L733ve3zhC19gdHR00z6kIlZLY6+240wqlcLlcpFMJne880rhoH00GgWW\nXWfq6uq25YGi0hC9awOBwJpV3kaQyWS4cOEC586dY3p6momJCUKhEKOjo3zxi1+koaGhoq+3i23F\nLvHtYm1kMhnkcnlJ8inlQyrdKyx34S3lOLMR95pi2EmxQeuFtHq1WCx5SlLxgUJ6HcvJkawFVKLK\nWw2iN2kkEqGrqytHql6vl1u3bnH48OGiGZG72LHYJb5dVB7FfEjj8XjewitWheUsvIV7NLFYbEPC\nme0Wr1QLot1YIpGgubk5z61HhPhAIX2o2GiO5FZBWuVVa49SHPepq6ujo6OjppTIr7zyCr/7u79L\nNpvlk5/8JJ/97Ge3+5QeFOwS3y62BtlsdsU4xUZ9SNcSzhQG0GYyGRYXF2tOvLJZFNqNrTfXsNAx\npRb2XEWISlSVSkVzc3PFCVlqadbZ2Zmbga0VZDIZnnjiCf78z/8cu93OJz7xCb785S/T19e33af2\nIGDXuWUXWwO5XJ43GA8b9yEV26harRaLxQLkC2cCgUDORUalUpFIJHJRMQ9KyyqZTOJyuUin0xt2\nylEqldTV1eUcTgoVkIWOKVuRsCCdN6xWlSeOQej1evbs2VNTVa6IK1eu0NnZSXt7OwBPPfUUP/7x\nj3eJr8qovU/CLh44qNVq1Gp1jrwKfUj9fn/ZPqSFjjPJZBKn00kikUCv15NOp7lz505NRDVtBtW0\nG5PJZLnfiWiWLnVMiUQieL3eVavrzUBMOlCpVFVJOhDjg4LBIO3t7TUtWHG73Tgcjtz/2+12rly5\nso1n9HBgl/h2seWohA+pIAj4fD68Xi8Wi4X29vbcv0mFM6FQiIWFhYoKZ6qNRCLB/Pw8crl8y+zG\nVktYKKyuC0cqym2RSqu8arWixdapRqNhZGSkJuZHd1F72CW+XdQE1uNDOj09zR/+4R/y+OOP85nP\nfGZF+2+1qKZ4PL7CULpWHGekxGCz2VY1DtgKFPNzlbZIQ6EQ8Xg8zwWo1HUUqzylUlm1Kk+8djsp\nPshut+cim2C5ArTb7dt4Rg8HdsUtVcCLL77IV7/6VSYmJvjOd77Dvn37tvuUHggsLS3x5S9/mR/9\n6Ed86lOf4tSpU0UrkGoIZ6oNqcjD4XDsmEpltcgr8SsWi+VcZapR5cXj8ZxVW3d3947a302n0zzx\nxBN885vfzIlbvvSlL9Hf37/dp/YgYFfcspUYGBjgK1/5Cl/4whe2+1QeKJw/f550Os3f//3f09DQ\nsMKH1Ov1lu1Duh7hTDXVjzvdbmy1yCtx3jCbzaJQKAiFQqTT6YqZm0vb3c3N/397dxMS1b/GAfx7\nnNEsX6ZxHN+QcJTrYC6UFtEiEHqxG1FEXl1oUkH0skjCUCkhyyCLIEOIaCF4LYiCui1c1I2o/hRE\ntaqLMjQtCtPGt+7oHCd1xrmLOucebczRmfGcmfl+IAiD+mnR4++c5/k+2cjIyIiorx3w80nH2bNn\ncfjwYXi9XlRUVLDorQDe+MKotrYWjY2NvPGtoMVySJcyxzb/0V6oE2dEUYzKuDHl1nKz2QyDwQCP\nx/NbBFsw4eZSUxMA5OXlcX0Q+cMbH8WGuLg4eWGs9K5EuhWKoigv3dXr9b8Fafu7Ffrrfgy2ccbr\n9cLhcEAURWRnZ88Z/Yh0UmOOTqeb8y5P+jr6213ob++eMtxc+feiXB+UmZmJrKysiLvlkfpY+Jbp\n4MGDGBkZ+e3jJ0+exLZt21Q4ES0kPj4eRqNxzjiFModUuTB2sRzSYBtnxsfH4XA4kJKSgvz8fM12\nli7V/FveYo05Cz1qlr6pcDqdctOHy+XCq1evUFRUhJycHKxevRqFhYV+k2uIAsHCt0xdXV1qH4GW\nSfleymw2A5ibQzoxMQGHwxFwDumfNrErbzNxcXHw+XwwmUwwGAxRU/SU4xfBhAfodDr5tg78/Dp6\nPB58/foVY2Nj6OzsxOfPn5GVlYWSkhJs3boV5eXlofxUKEaw8BHh53+6BoNBfqQ5P4d0aGjotxzS\nhQKglbeZtWvXyjvfpEYbqRiGu3Em3JTNJeEYvxAEAYIgQK/Xo7a2Fnl5eUhMTITdbsf79+/hdDpD\n9mdRbGFzSxg8efIEFy5cwNjYGFJTU1FUVITOzk61j0VBWmoO6cjICCYmJgAA2dnZc+YNA2mc+dPy\nWbVJewAFQUB2dnZYRgikx8JGoxG5ubma/aaA40uaxZBqonBQ5pCKogi32w1BEPD48WPcu3cP7e3t\n2LBhgyZWNYWC8paXnp4Oo9EY8sIsNf+43W7k5eXJGaNa9enTJwiCgJaWFnZxawu7OmMdV5+Ex/wc\nUrvdjqamJuj1ely9ehVGoxEfP34MKId0ocYZqRiqnTgj3fIAhC0I3OVyYXBwEAaDAevXr4+I96AF\nBQVqH4GWiIUvBni9XrS2ts5ZfbJlyxYmwIfB69evUVVVhcrKSvmWt9QcUiWpcUa5WWGxMYBQJ84o\nA7PDdctTrg/Ky8uT37UShQMLXwzg6pOVs3///t8+tpQcUmUB8zcYH+gYQKgaZ6anpzEwMAAgfLc8\nURTljfJaXR/E8aXoor1/YRRyXH2iLcrilZ6eDuBn8VI2zkiD8YHkkPobA/C3by+QjlSJ8pZnMpmQ\nlpYWlluetDhY6+uDOL4UXVj4iDRAp9P5XRa73BzShRJnfvz4AVEUMTIyIke5zW+ckeLAfD5f2NYi\nSaHciYmJXB9EK46FLwZw9UnkkYpXWlqafBOan0M6OjoacA6pv8YZj8cj3wqlxhlBEDA7O4ukpCSk\np6eH/NGmcn1Qbm5uSBfsqkU5vnT06FGOL0UAjjPEAK4+iV7KHFKXywW32x1QDul80rs8r9eL1NRU\nuZtUGeUWbONMJK8PoojEOb5Y9+LFC1y8eFFefXL8+HG1j0RhMD+HVBTFP+aQzs7O4tu3b3C5XH7f\n5SkbZ6QfS22cUc7+5eTkwGw2R/wtjyICCx9RrFLmkIqiiMnJSTkwu6OjA5mZmTh//nxAq30WSpxJ\nSEiYUwyld4/S+0JBEGCxWMLyvpBoASx8pG2nT5/G8+fPYTKZ0NPTo/Zxotrs7Czu3LmDjo4O7N27\nF7t27YLH41lS1+f83085W2i329HS0gKLxYKCggJs3LgRZWVl8vgF0Qph4SNte/v2LdasWYOmpiYW\nvjAbHx9HQ0MDTp06hcLCQgBLzyH9k5mZGfT29qKvrw/Dw8Po7e3Fhw8fUFxcjFu3boX70yOSsPCR\n9vX39+PYsWMsfBrhL4dUikuT3hUq49J8Ph+cTieGhoZgNpuRk5Mj/5rX64XT6dTMrN7ly5fx7Nkz\nxMfHY926dWhra5PXSlHUYOEj7WPh0zafzzdnnEIURXg8HiQmJmLVqlWYmpqC1+uFxWKRh+m16uXL\nl9i0aRP0ej2uXLkCAGhoaFD5VBRiDKkmouAIgiDPAmZkZAD4fw6p0+lEQkICLBaLZtcHKW3evFn+\neWlpKR49eqTiaWilsfAR0bLNzyGNRPfv38fOnTvVPgatIBY+IopKgQRL37hxAzqdDnv27Fnp45GK\n+I6PNKG+vh5v3rzB9+/fYTKZcOLECVRWVqp9LIpiDx48wN27d9HV1RXQDCNFHDa3EBFJ/vrrL1y6\ndAm3b9/WTKcphRwLH1EwBgcH0djYiNHRUQiCgKqqKhw4cEDtY9Eybd++HdPT0/K7yZKSErS2tqp8\nKgoxFj6iYAwNDWF4eBjFxcVwuVyoqKjA9evXucyXSLsWLHza7zsm0oCMjAwUFxcDAJKTk5Gfnw+H\nw6HyqYhoOVj4iJaov78ffX19KCkpUfsoRLQMLHxESyCKIurq6nDmzBkkJyerfRwiWgYWPqIAzczM\noK6uDrt370Z5ebnaxyGiZWLhIwqAz+dDc3Mz8vPzcejQIbWPQ0RBYFcnUQDevXuHmpoaFBYWylmU\n9fX1KCsrU/lkseHatWt4+vQp4uLiYDKZ0NbWhszMTLWPRdrGcQYiilwul0t+p9rd3Q273c65O1oM\ntzMQxYKpqSnU1NRgenoaXq8XO3bsQF1dndrHCpqykcjtdge0GZ5oIbzxEUURn8+HyclJJCUlYWZm\nBtXV1WhubkZpaanaRwtae3s7Hj58iJSUFHR3dzNqjBbDR51EscbtdqO6uhrnzp2LiJnDQLYpAMDN\nmzcxNTUVFTdZCisWPqJY4fV6sW/fPnz58gXV1dVRt1l8YGAAR44cQU9Pj9pHIW1bduEjoghltVrX\nAvgXgBM2m+0/ap8nGFar9W82m+3jr5+fAFBms9n+ofKxKEKxuYUoStlstv9ardZnAP4OIKILH4BL\nVqvVCmAWwGcAx1Q+D0Uw3viIoojVajUDmPlV9FYD+DeAyzabjc8FiX7hjY8oumQD+KfVatXhZzLT\nPRY9orl44yMiopjCrE4iIoopLHxERBRT/gfbF7KDp7KRPAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f33a423cb90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "\n",
    "# 获取X, 设置x0 = 1\n",
    "ones = pd.DataFrame({'ones': np.ones(len(data))})\n",
    "X = pd.concat([ones, data], axis=1).iloc[:, :-1].as_matrix()\n",
    "# 获取Y\n",
    "Y = data.iloc[:, -1:].as_matrix()\n",
    "fig = plt.figure()\n",
    "ax = Axes3D(fig)\n",
    "x1 = X[:, 1]\n",
    "x2 = X[:, 2]\n",
    "y = Y[:, 0]\n",
    "\n",
    "# 样本数据\n",
    "ax.scatter(x1, x2, y)\n",
    "ax.set_xlabel('square')\n",
    "ax.set_ylabel('bedrooms')\n",
    "ax.set_zlabel('price')\n",
    "plt.show()\n",
    "\n",
    "# 样本数据+回归模型\n",
    "fig = plt.figure()\n",
    "ax = Axes3D(fig)\n",
    "ax.scatter(x1, x2, y)\n",
    "y_ = x1 * final_theta[1] + x2 * final_theta[2] + final_theta[0]\n",
    "ax.plot_trisurf(x1, x2, y_, linewidth=0.2, antialiased=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 用矩阵计算theta \n",
    "![avatar](img/4.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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QdwitXuONipHJZPDMM8/g3nvvxR133GHoay154csXeTSS8KXTafh8PiSTSdjt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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f339fa7d710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def lineRegression(X, Y):\n",
    "    # 逆矩阵\n",
    "    v = np.linalg.inv(np.dot(X.T, X))\n",
    "    theta = np.dot(np.dot(v, X.T), Y)\n",
    "    return theta\n",
    "\n",
    "final_theta = lineRegression(X, Y)\n",
    "# 样本数据+回归模型\n",
    "fig = plt.figure()\n",
    "ax = Axes3D(fig)\n",
    "ax.scatter(x1, x2, y)\n",
    "y_ = x1 * final_theta[1] + x2 * final_theta[2] + final_theta[0]\n",
    "ax.plot_trisurf(x1, x2, y_, linewidth=0.2, antialiased=True)\n",
    "plt.show()"
   ]
  }
 ],
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